Module7PROJECT MANAGEMENT

Introduction

Network analysis is a common topic in quantitative business texts and much theoretical research has been done in the area. Hundreds of theoretical academic papers have been written about such concepts as the shortest-path problem, the minimal spanning tree problem, and the maximal flow problem. Fortunately, many concepts in network theory have translated to useful real-world applications in the fields of information theory, cybernetics, transportation systems, production management, and project management. In this module we will concentrate on project management.

Chapters in a business text dealing with this topic many may be titled project management, project scheduling, or PERT/CPM. Regardless, (by the way "irregardless" is not a word) they all deal with basically the same thing - the efficient scheduling and management of complex projects.

What is a project? Examples actually work better than a formal definition. The Egyptians were involved with project management when building a pyramid. Sidney, Australia planned the 2000 Olympics - a project. Philadelphia hosted the republican political convention - another project. In business, the introduction of a new product is typically a project as is opening a new store or implementing a computerized accounting system. In your personal life, planning a wedding or building a new home, would be examples of projects. We can generalize and define a project to be a collection of events or activities, related to each other over time, whose purpose is to achieve a specific goal.

At sometime in your career you will be part of a project team or maybe even the project manager. Any association with a formal project will probably necessitate some involvement with estimating time and cost figures. Much advanced planning is mandatory. Time and cost data are constantly being estimated, calculated, updated, refined, agonized over, and reported. Projects delivered (a term frequently used)"ahead of schedule and under cost" may get you promoted; careers have been ruined by being "behind schedule and with cost overruns."

There are literally dozens of software programs to help decision-makers manage the intricacies of large projects. You will undoubtedly use one of these off-the-shelf programs to aid in the management and administration of a project. With these programs you simply(?) input the data and use the reports generated by the software to make critical decisions. As discussed in the introduction to this course, we will not be using a specialized program but continue to use Excel to analyze project data. Yes, it is very cumbersome and not practical in the real world but it will give you an appreciation of what goes on inside the "black box" of typical specialized project management software.

You noticed the acronyms PERT and CPM in an earlier paragraph. In the late 1950's the US embarked on the Polaris project. The goal was to combine three complex technologies into an integrated weapons system. A basic submarine is complex, then add a nuclear power plant, and finally add the nuclear ballistic missiles and associated launching system. Now, that was a project! It was huge, controversial, unimaginably complex (200 prime contractors and 9000 subcontractors), and a resounding success - on time and at cost. Many who were involved or have studied the project credit a methodology called PERT (Program Evaluation and Review Techniques), which was developed by the Navy Special Projects Office and the management-consulting firm of Booz, Allen, Hamilton. Even today many government agencies contractually require the use of PERT.

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Analysts at Remington Rand and DuPont developed CPM (Critical Path Method) separately in 1957. It differs from PERT in the details of how time and cost are handled. PERT is considered to be more deterministic; CPM more probabilistic. Over the years the distinctions between the two have blurred as the best features of both have been integrated. The premise of PERT/CPM is "management by exception". The Apollo project is a good example. In the 1960's the US was committed to putting a man on the moon by the end of the decade. Hundreds of thousands of activities and tens of thousands of events were involved. PERT/CPM techniques enabled project managers to identify the few hundred activities that were "critical" to keeping the project on track and monitor these critical activities continuously.

Enough background - let's do some PERT/CPM

I have recently been tasked to start a new sequence of courses for a Masters of Science in E-Business program. Lots of coordination is required among different administrative, faculty, and staff organizations. A teaching location must be located, curriculum designed and courses developed, hardware and software purchased and installed, instructors assigned, and potential students screened. Each of these activities involves dealing with different organizations and personnel. Of course, we would like to get the program started as soon as possible, but planning is complicated because of all the interdependence of activities. Here are 4 questions that I would like to answer.1. What is the soonest that classes could start?2. What is the start and completion date for each activity?3. What activities are critical to meeting the project deadline?4. If an activity is non-critical, how much delay can be incurred?

The first step in the process is to define the activities and establish the proper precedence relationships. In the real world this is usually a group effort and is the most important step in the process. Errors or omission here can lead to grossly inaccurate results. Here is my activity list. It contains the activity, a brief description of the activity, and the immediate predecessors of each activity.

Activity Description Predecessors

A Select site for classes

B Define curriculum

C Plan courses B

D Order hardware/software A, C

E Install hardware/software D

F Determine personnel requirements C

G Hire adjuncts F

H Modify teaching assignments F

I Select students B

J Prepare classes H, E, G

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PERT Network Diagram - To get a better feel for the interrelationships among activities it is helpful to sketch a diagram of the project in network form. Our network is made up of arrows (called arcs or branches) and nodes. We will draw two networks. The first is called AON (activity on nodes). Most students find these quite easy as they represent the project in a straightforward, common sense, logical manner. Unfortunately, the AON representation is not easily converted to a format that is computer friendly. If we use an AOA (activity on arcs) depiction, the information is easily input into software programs due to the way users are required to enter activity start and end data. It is a little more difficult to sketch, however. The majority of textbooks use the AOA approach but we will use the AON approach in these notes.

Activity on Nodes

Activity Description Predecessors

A Select site for classes

B Define curriculum

C Plan courses B

D Order hardware/software A, C

E Install hardware/software D

F Determine personnel requirements C

G Hire adjuncts F

H Modify teaching assignments F

I Select students B

J Prepare classes E, G, H

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For comparison, here is an Activity on Arcs representation of the same project.

Activity Description Predecessors

A Select site for classes

B Define curriculum

C Plan courses B

D Order hardware/software A, C

E Install hardware/software D

F Determine personnel requirements C

G Hire adjuncts F

H Modify teaching assignments F

I Select students B

J Prepare classes H, E, G

Note the dummy activities between nodes 4 and 2 and between 8 and 7.

4

9

8

76

5

4

3

2

1

CB

F

D

H

I

E

G

J

A

We still have not done any analysis that will help us answer the four questions posed earlier, but the questions all have to do with time. Let's enter the time data. After much deliberation, and many phone calls and emails, the project team has agreed upon the time it will take to complete each activity. This data is deterministic.

Activity Description Predecessors Time (weeks)

A Select site for classes 3

B Define curriculum 5

C Plan courses B 3

D Order hardware/software A, C 4

E Install hardware/software D 8

F Determine personnel requirements C 2

G Hire adjuncts F 4

H Modify teaching assignments F 2

I Select students B 5

J Prepare classes H, E, G 3

Now use the time data to determine the Earliest Start Time, Earliest Finish Time, Latest Start Time, and Latest Finish Time for each activity. Once we have these times we can determine which activities are critical and which may be delayed (and by how much) without impacting the end result.

The activities that are critical are said to be the "critical path". The critical observation is that if any activity on the critical path is delayed or takes longer than expected, then the project will not complete by the planned completion date. Activities that can be delayed are said to have "slack time"

We will first do this by hand then develop an Excel spreadsheet to calculate the results. Your spreadsheet results should look something like this.

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Activity Description Time EST EFT LST LFT Slack On critical path?A Select site for classes 3 0 3 5 8 5 NoB Define curriculum 5 0 5 0 5 0 YesC Plan courses 3 5 8 5 8 0 YesD Order hardware/software 4 8 12 8 12 0 YesE Install hardware/software 8 12 20 12 20 0 YesF Determine personnel requirements 2 8 10 14 16 6 NoG Hire adjuncts 4 10 14 16 20 6 NoH Modify teaching assignments 2 10 12 18 20 8 NoI Select students 5 5 10 18 23 13 NoJ Prepare classes 3 20 23 20 23 0 Yes

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We have answered the four questions.

1. What is the soonest that classes could start? In 23 weeks.2. What is the start and completion date for each activity? See network and/or spreadsheet.3. What activities are critical to meeting the project deadline? B, C, D, E, J4. If an activity is non-critical, how much delay can be incurred? A, 5 weeks; F, 6 weeks; G, 6 weeks;

H, 8 weeks; I, 13 weeks.

The Next Level of Analysis - Variability in Activity Times

It would be pretty naive of us to assume that our point estimates (deterministic) of the activity times are completely accurate. It is expected that a good analyst would provide a range of times for each activity and perhaps even associated probabilities. To fine-tune initial results a common approach is to develop three time estimates. The analyst (and project manager) should interview personnel who have enough knowledge and experience with each activity to produce the following three estimates of time.

1. The optimistic time (to) - if everything goes perfectly then the activity could be complete in this amount of time. The minimum time possible for any activity.

2. The most probable time (tm) - The time normally required to complete an activity given the usual problems and delays. The most likely time.

3. The pessimistic time (tp) - This is the time an activity will take if significant problems occur. Remember Murphy's Law, when it is in effect this will be the time to complete an activity.

Here is that information for the MS in E-Business project.

Activity Description Optimistic Most likely Pessimistic

A Select site for classes 2 3 5

B Define curriculum 3 5 7

C Plan courses 2 3 5

D Order hardware/software 3 4 9

E Install hardware/software 4 8 14

F Determine personnel requirements 1 2 3

G Hire adjuncts 2 4 8

H Modify teaching assignments 1 2 4

I Select students 3 5 6

J Prepare classes 2 3 5

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Consider activity G, Hiring adjunct professors. If we hire an adjunct we have used for previous courses it may take only two weeks to complete the process as we have all of his/her paperwork on hand, have already conducted an interview, etc. and all that remains is to prepare and sign a contract. On the other hand, if we want to hire a new instructor it may take 4 weeks to advertise, get resumes, conduct interviews, etc. for all the applicants. If we go through the entire process and the selected individual accepts another position, then we have to go through the entire process again and it may take as long as two months. So 2 weeks, 4 weeks and 8 weeks are example of optimistic, most probable, and pessimistic times. (to = 2, tm = 4, tp = 8)

In the original PERT approach, the procedure for estimating the expected value of the activity was based on the premise that activity times are random variables with a particular probability distribution. Both research and empirical results have shown the beta distribution to be an excellent choice. (The triangular distribution is similar and has also been used.)

What is beta distribution? Unlike the normal distribution, the beta distribution has a minimum and maximum value and is capable of assuming a wide variety of shapes. The expected value of the time for an activity to complete (te) using a beta distribution is

(the denominator, 6, is a constant)

For the adjunct hiring

You can estimate the standard deviation for a beta distribution by

Management has let it be known that it would like to start the first class in the E-Business Masters program in 6 months, 26 weeks to be exact. Use the information given to determine the probability of completing a project by that date. This may require you to reach way back in your memory banks.

1. Let T be the total time of the critical path activities.

2. Given the optimistic, most likely and pessimistic times, we need to find the probability that the project will complete in 26 weeks or less. Or P(T 26)

3. Make the following assumptions:

a. activity times are independent random variables

b. random variable T has an approximately normal distribution. (We can do this because of the Central Limit Theorem.)

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To find P(T 26), we need the standard deviation of T. We can find the variance of T by summing the variances of the times for each activity on the critical path,

Var(T) = Var(B) + Var(C) + Var(D) + Var(E) + Var(J)

(Recall the standard deviation is the square root of the variance. An oft forgotten statistical concept is that standard deviations don't add. We must sum the variances of individual parts then take the square root to find the standard deviation.) There is an explanation at http://www.interventions.org/pertcpm.html and http://www.baskent.edu.tr/~kilter/academic/isle542/isle542_08.ppt

Var(T) = .44 + .25 + 1 + 2.78 + .25 = 4.73 ====> StDev(T) = 2.17

T = 24.33 weeks ( the sum of the expected times for activities B, C, D, E and J)

P( T 26 ) = P(Z .77) = 78% You could report that there is about an 80% chance that the project will be finished on time (26 weeks)

A spreadsheet for the data might look something like this.

PERT is not only a planning system. Using the information from the above analysis, we can monitor the progress of the project. Management can compare the actual activity times as they occur and compare them to those projected in the planning process. If critical activities fall behind then action must be taken to remedy the situation. Often times this involves dedicating more resources to a troublesome activity. This is not unusual as projects are often new or unique and there is a relatively small experience base. Typically, to decrease the time for a given activity it is necessary to increase the resources allotted to that activity. Additional resources almost always translate into increased costs. (An aside: The project management triangle is made up of schedule, cost, and quality. To improve on any one of the three, it is necessary to give up something on one or both of the other two.)

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Include Cost Considerations

We have already mentioned that successful projects meet both time and cost predictions. We have a good idea of how to analyze the time requirements now we need to consider the dollar cost factors. There are three basic cost categories involved in most projects - direct costs, indirect costs, and penalty costs. Direct costs include labor, material, and other costs directly related to completing activities. Activity times may be shortened by applying additional resources such as overtime, special equipment, or more personnel. Obviously, as additional resources are added, the direct costs increase. Indirect costs are those costs that support the project, overhead costs, so to speak, such as administration, financial, security, maintenance, and depreciation. Shortening the project time may decrease these costs. Typically, the shorter the project, the lower the indirect costs. A project may also involve penalty costs; these are incurred if the project extends beyond a specific date. (Aside: In some contracts a bonus may be provided for early completion.)

It is intuitive to most students that time and money are related. This is true in most projects. We can "throw money" at a project (increase the direct costs) and frequently get activities done quicker. This is called "crashing" an activity. In our previous example, we expect our hardware order (Activity D) to take 4 weeks. Part of that is delivery time and we could pay a premium to expedite our order, say airfreight instead of ground transportation. For most situations there is a minimum limit; you can't continue to improve time indefinitely just my spending more money. For our hardware delivery, the minimum time might be two weeks because we still have to place the order, get the material from the warehouse, load onto trucks, transport to the air terminal, load the aircraft, etc.

Some clarification. You probably noticed that the two weeks is less than the three-week optimum time in the original problem. The optimum times consider only "standard practices" or "default values" that would be typical for an activity. For example, it typically takes you 17 minutes to drive to work, park, and get to your office. If you hit all the lights just right, find an awesome parking place right away, and don't get caught in an elevator traffic jam, you might make it to your office in 13 minutes. If your usual route is blocked by an accident and there are no parking places to be found, it might take you 25 minutes. These would be the typical and standard, te, to, and tp But, if you woke up at 8:30 am and a key presentation started at 8 am, you might speed to work, only pause for red lights, park illegally, and run to your meeting. These would be extraordinary measures probably incurring increased costs.

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An example with costs involved.

Since we are just interested in the quantitative analysis aspect, time and cost data are provided without a specific setting. For this project the indirect costs are $8000 per week. Also, there is a penalty cost of $20,000 per week after week 65.

Activity Immediate

Predecessor(s)Normal

Time (wks)

Normal Cost ($)

Crash Time (wks)

Crash Cost ($)

Max Crash Time

Crash Cost per

wks

A 12 12000 11 13000 1 1000

B 9 50000 7 64000 2 7000

C A 10 4000 5 7000 5 600

D B 10 16000 8 20000 2 2000

E B 24 120000 14 200000 10 8000

F A 10 10000 6 16000 4 1500

G C 35 500000 25 530000 10 3000

H D 40 1200000 35 1260000 5 12000

I A 15 40000 10 52500 5 2500

J E,G,H 4 10000 1 13000 3 1000

K F,I,J 6 30000 5 34000 1 4000

Here are the questions we want to answer.

1. What is the normal project time, cost, and critical path?

2. What is the minimum cost schedule and critical path?

3. What is the minimum time schedule and critical path, regardless of cost?

Before we start the analysis, there is one additional assumption to be made. This artificiality is seldom true in the real world. In the example data above, I have assumed that improvement gains in time are related to costs by a linear function. For example, I can expect to compete the activity F in 10 weeks at a cost of $10000, in 9 weeks if I spend $11500, 8 weeks if I spend $13000, etc. I have assumed that I can decrease the activity time one week for each $1500 spent up to 4 weeks. In real world situations, it is typical to get "more time for the buck" as you begin to decrease time and it gets harder and more expensive as you try to squeeze the last bit of efficiency out of the system. Actual situations are usually non-linear.

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It is fairly tedious to conduct a minimum cost analysis by hand but worthwhile to do it once in your lifetime. In the future you will use software packages.

Construct the AON network so you can visually identify all possible paths through the project and compute their lengths.

A-I-K: 33 weeks

A-F-K: 28 weeks

A-C-G-J-K: 67 weeks

B-D-H-J-K: 69 weeks

B-E-J-K: 43 weeks

You should identify the critical path as B-D-H-J-K and a project length of 69 weeks. If the project takes 69 weeks in normal time the direct costs are $1,992,000, indirect costs of $552,000 (69 x $8000) and $80,000 (4 weeks x $20,000) in penalty costs.

If all activities on the critical path were crashed, that path duration would be 56 weeks. If all activities on A-C-G-J-K were crashed, this path length would be 47 weeks. Since the other three paths are already less than these are, you may disregard them in the analysis.

The basic approach is to crash the lowest cost activity (or combination of activities) on the critical path(s) keeping in mind that as activities are crashed other paths may become critical and the cost of crashing must continue to provide a cost improvement. The cheapest activity to crash on the critical path is activity J at $1000 per week and J can be crashed a maximum of 3 weeks. Note: You may not always be able to crash an activity the maximum number of weeks because other paths may become critical. A good approach is to look at crashing activities one week at a time and see what the effects on the project are. The new path lengths are:

A-C-G-J-K: 64 weeks

B-D-H-J-K: 66 weeks

By reducing the critical path by 3 weeks we have saved $60,000 ($20,000 x 3) in penalty costs and $24,000 ($8000 x 3) in indirect costs for total of $84,000. It cost us $3000 ($1000 x 3) in crashing costs to reduce the project length by 3 weeks, so the net savings is $84,000 - $3000 = $81,000. The total projects costs are now $2,624,000 - $81,000 = $2,543,000.

For the next interation, crash activity D by the maximum of 2 weeks at $2000 per week. The saving are $20,000 for one week (we are now out of the penalty period) and $8000 for two week with $4000 crashing costs for a net savings of $32,000 ($20,000 + $16,000 - $4000). The project cost is now $2,511,000. The new path lengths are:

A-C-G-J-K: 64 weeks

B-D-H-J-K: 64 weeks

Notice now that we have two critical paths so to reduce the project length activities on both paths must be crashes. We may crash one activity common to both paths or an activity unique to each path.

Here are the alternatives to be considered: Crash (A and B), (A and H), (C and B), (C and H), (G and B), (G and H), or K (which is common to both paths). The cost to crash all alternatives except (C and B) at $7600 per week and K at $4000 per week cost more than $8000 per week potential saving so we can remove these from considerations. So, crash K the maximum possible amount - 1 week. The paths are now:

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A-C-G-J-K: 63 weeks

B-D-H-J-K: 63 weeks

The project cost is now $2,511,000 - ($8000 - $4000) = $2,507,000

The last step - Crash B and C 2 weeks simultaneously at a cost of $7600 per week yielding a net saving of $800. The minimum cost project schedule is $2,506,200 with a project length of 61 weeks.

The final question to be answered is the minimum time schedule. We could crash all activities but this would be wasteful. The correct approach is to continue the technique for the minimum cost schedule, as we did above, until no further time improvement. Finding the minimum time schedule (at the minimum cost) is left as an assignment.

It was mentioned earlier in the module that PERT/CPM analysis is both a planning tool and monitoring tool. The PERT/CPM can be used to monitor both cost and time progress. Here is an example for the MSIS project.

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Budget demands vs time

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

2000000

0 10 20 30 40 50 60 70weeks

$

Latest start time total cost schedule

Earliest start time total cost schedule

Area of feasible budgets for project costs

$621,897

$438,320

Assignment:

For a maximum grade of B- complete the following exercise.

Mid-Penn Builders has identified the following 10 activities that take place when building custom homes:

Activity ID Activity Predecessor(s) Expected Time (days)

A Foundation - 6

B Frame walls and ceiling A 10

C Install roof trusses B 4

D Wiring and plumbing B 8

E Windows B 4

F Install dry wall D, E 6

G Brick exterior E 10

H Install skylights C 6

I Slate roof H 16

J Paint F, G, I 4

1. Use the information given for Mid-Penn Builders to complete the following activities.

a. Construct the AON network diagram for the project.

b. For each activity, give the earliest start, earliest finish, latest start, latest finish, and slack time. Identify the critical path(s).

For a maximum grade for B

1. Complete the B- assignment.

2. Use the below information and an Excel spreadsheet to compute a table of the expected activity time and the standard deviation for each activity. Use the information to develop an Excel spreadsheet of PERT analysis and determine the probability that the critical path will be completed within 40 days.

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Mid-Penn Builders has conducted additional analysis and determined the following times.

Activity ID Activity Optimistic time Most probable time Pessimistic time

A Foundation 4 6 8

B Frame walls and ceiling 6 10 14

C Install roof trusses 2 4 6

D Wiring and plumbing 8 8 8

E Windows 2 4 6

F Install dry wall 4 6 8

G Brick exterior 2 6 34

H Install skylights 2 4 18

I Slate roof 8 16 24

J Paint 4 4 4

For a maximum grade for B+

1. Complete the B assignment.

2. Your company has just received an order for some specially designed software. The contract states that you will incur a $100 per day penalty for each day the software is not delivered after day 12. Your indirect costs are $200 per day. Direct cost data and activity precedence relationships are given below.

Activity ID Immediate Predecessor Normal Time

Crash time

Normal Cost ($)

Crash Cost ($)

A None 4 3 1000 1300

B None 7 4 1400 2000

C Nome 5 4 2000 2700

D A 6 5 1200 1400

E B 3 2 900 1100

F C 11 6 2500 3750

G D,E 4 3 800 1450

H F,G 3 1 300 500

Use this data to recommend a completion date that will minimize your costs.

3. Determine the minimum time schedule (at minimum cost) for the crash cost example in the notes.

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For a maximum grade of A-

1. Complete the B+ assignment.

2. Use the cost data below and early start/late start data from the B- level assignment to construct a graph of cumulative expenditures versus time for the Mid-Penn Builders project. To construct the graph you must have your spreadsheet calculate the total expenditures at the end of each day for two separate circumstances. Each circumstance will give you a line on the graph.; the first is for the situation where you start and finish every activity at the earliest time possible, the second is if you start and finish every activity at the latest time possible. You will need to calculate the anticipated daily expenditures for each activity.

Activity ID Activity Normal Time

Normal Cost ($)

A Foundation 6 4000

B Frame walls and ceiling 10 10000

C Install roof trusses 4 3000

D Wiring and plumbing 8 6000

E Windows 4 9000

F Install dry wall 6 4400

G Brick exterior 10 9000

H Install skylights 6 1600

I Slate roof 16 2600

J Paint 4 8000

For a maximum grade of A

1. Complete the A- assignment.

2. A small shipyard has been contracted to accomplish repairs to a navy ship. The ship had an oil pump failure that resulted in damage to a main gearbox assembly that subsequently caused damage to one of the ship's turbine engines. The Navy needs the ship back in service as quickly as possible. The damaged turbine must be prepared to be lifted off of the ship with a crane and that prep will take about 4 hours. The shipyard is very experienced at turbine exchanges and can remove a turbine and replace it with a new one in 36 hours. The crane must remain dedicated to the turbine job for the entire 36 hours. While the turbine is being replaced, the fuel lines have to be replaced (18 hours), the fuel pump overhauled (8 hours), a main bearing machined and reseated (12 hours), oil system flushed (18 hours), relief valves reset (5 hours), and the shaft realigned (8 hours). These 6 repairs can be done simultaneously and can be worked on while the turbine is

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being exchanged. Once these 6 repairs are complete and the new turbine on board, the turbine assembly must be tested which will take about 12 hours.

The gearbox assembly also has to be removed from the ship and replace with a new one. Once the gearbox is prepared for removal (this will take about 8 hours and can be accomplished at the same time the turbine is being prepped for removal), it will take about 24 hours for a crane to remove it and load the new one. Again, the crane must be dedicated to this job for the entire 24 hours. While this exchange is taking place, four other jobs can be completed on the ship. The oil must be cleaned up (12 hours), the oil pump must be repaired (12 hours), the control valves will have to be changed out (8 hours) and some oil lines will have to be replaced (4 hours). These four activities can take place simultaneously. Once the gearbox is in place and these four associated activities completed, the unit has to be tested for four hours.

The turbine work and gearbox work do not interfere with each other. Once both the gearbox and turbine work are completed they must be tested as a unit for 4 hours.

The Navy wants the ship back as fast as possible. They have written a cost plus contract with time incentives. For every hour under 60 hours the incentive is $4000. The problem is the crane; the shipyard only has one. A neighboring competitor has a floating crane that it will lease at an exorbitant price since it didn't get the contract. The lease is $5000 base plus $1000 per hour. The shipyard's overhead costs on this project are estimated to be $1200 per hour. This shipyard would like to "show its stuff" to the Navy and get the ship ready as quickly as possible but it can't afford to lose money on this project. Conduct an analysis that supports a decision to lease or not lease the second crane.

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